Solitary wave solutions with stability, bifurcation, sensitivity and chaotic analysis of the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation using beta derivative

The space-time fractional Yu-Toda-Sasa-Fukuyama equation (YTSFE) is widely used to describe elastic quasi-plane waves in a two-layer fluid system, characterizing the behavior of the interface between two immiscible fluid layers of differing densities, relevant to interfacial wave dynamics in such systems. In this work, we explore solitary wave solutions to the (3+1)-dimensional space-time fractional YTSFE and analyze in detail using the extended modified auxiliary equation mapping technique. We construct a variety of solitary wave solutions to this equation, including trigonometric, rational, and hybrid solutions. The solutions include a range of waveforms such as kink, anti-kink, general, and plane-type solitons, which hold numerous applications in physical sciences and engineering. The solutions of this work have been compared with existing results, and new solutions have been identified. The effect of fractional order derivative on the soliton has been shown graphically. The stability, bifurcation, chaotic, and sensitivity analysis of the dynamical system of the governing model have been assessed. The graphical representations of the solutions are provided in 2D, 3D, and contour formats, using MATLAB with appropriately selected parameter values. The method proves to be effective and efficient for investigating nonlinear integrable equations, confirming its potential for addressing the space-time fractional YTSFE.